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Bimetallic Strip Bending Angle

  • Thread starter tejas710
  • Start date
  • #1
3
0
Hi! There is a thermodynamics problem which I seem to be able to understand, yet unable to solve. If someone can me with it I would appreciate it.

Homework Statement


A Bi-metallic strip is straight at T= T0. It curves as it is heated up due to unequal expansion of two metals. The strip is made up of iron (a = 1.2e-5) and zinc (a = 3.1e-5). The question asks to calculate the bending angle when the original length of the strip is 100mm and with thickness of 1 mm.


Homework Equations


The linear expansion equation: L = L0(1 + a(T2 - T0))


The Attempt at a Solution


The substituted equations: LI = (100)(1 + (1.2e-5)([tex]\Delta[/tex]T)
LZ = (100)(1 + (3.1e-5)([tex]\Delta[/tex]T)

From here I use the formula s = r[tex]\theta[/tex]
and get [tex]\theta[/tex] = (3.8e-3)([tex]\Delta[/tex]T)

I am not sure how to proceed from here because the question asks for a numerical answer but that seems impossible without the temperatures given.
 

Answers and Replies

  • #2
LowlyPion
Homework Helper
3,090
4
Welcome to PF.

If they give no temperature rise, then leave your answer in terms of ΔT as you have.
 
  • #3
3
0
Thanks. I guess I will leave it as an expression.
 
  • #4
5
0
Poptor, eh?
 
  • #5
5
0
Sorry for the double-post, but also.. I don't understand your solution.

What does s=r*Theta have to do with this question.. and how does that lead to your solution?
 
  • #6
LowlyPion
Homework Helper
3,090
4
The displacement of the end is given by the angle times the radius for small angle displacements.
 
  • #7
5
0
Oh.. what exactly is the radius in this question?
I guess it's just that he said:

3. The Attempt at a Solution
The substituted equations: LI = (100)(1 + (1.2e-5)(LaTeX Code: \\Delta T)
LZ = (100)(1 + (3.1e-5)(LaTeX Code: \\Delta T)

From here I use the formula s = rLaTeX Code: \\theta
and get LaTeX Code: \\theta = (3.8e-3)(LaTeX Code: \\Delta T)


I sense a really big logic gap missing..

Otherwise, I thought the appropriate formula was:

Theta = length / thickness * (a1 - a2)*(T2-T1)

Where a1 and a2 are the expansion coefficients, and T2 and T1 are temperatures.

Excuse my ignorance, and thanks for the help.
 

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